Aerodynamic forces and vortical structures of a flapping wing at very low Reynolds numbers

Reynolds number (Re) for miniature insects is in the range of 80-10. Here, we study how the aerodynamic forces change in this Re range when the flapping mode commonly used by larger insects is employed and explore the physical reasons for the change. We find that at Re below ∼70, the lift decreases and the drag increases rapidly with decreasing Re. This can be explained as follows. In this Re range, the viscous effect becomes very large. Much of the clockwise (CW) vorticity in the leading-edge vortex is diffused to be far above the wing and moves backward relative to the wing, and some of the counterclockwise (CCW) vorticity in the boundary layer at the lower surface of the wing is diffused to be more forward, and the boundary layer becomes thicker. This results in less CW vorticity moving with the wing and less CCW vorticity moving backward of the wing, causing a reduction in the time rate of change in the vertical component of the total first moment of vorticity, i.e., the reduction in the lift. The above changes in vorticity distributions also increase the vertical distance between the CW vorticity and the CCW vorticity, causing an increase in the time rate of change in the horizontal component of the total first moment of vorticity, i.e., the increase in the drag. These results show that if miniature insects flap their wings as the larger ones do, the aerodynamic forces required for flight cannot be produced and new flapping mode must be used.